What is Input/Output Logic?

  • David Makinson
  • Leendert van der Torre
Part of the Trends in Logic book series (TREN, volume 17)


We explain the raison d’être and basic ideas of input/output logic, sketching the central elements with pointers to other publications for detailed developments. The motivation comes from the logic of norms. Unconstrained input/output operations are straightforward to define, with relatively simple behaviour, but ignore the subtleties of contrary-to-duty norms. To deal with these more sensitively, we constrain input/output operations by means of consistency conditions, expressed via the concept of an outfamily. However, this is a more complex affair, with difficult choices between alternative options.


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  1. 1.
    There are many examples in the literature. Most of them involve ingredients that, while perfectly natural in ordinary discourse, are extraneous to the essential problem and thus inviteGoogle Scholar
  2. false analyses. These ingredients include defeasibility, causality, the passage of time, and the use of questionable rules such as CT and OR in deriving output. We have chosen a very simple example that avoids all those elements. There is one respect in which it could perhaps be further purified: under input d, the output is not only inconsistent with the input, but also itself inconsistent. This matter is discussed at the end of Section 5.Google Scholar
  3. 3.
    Cf [AlcGärMak85].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • David Makinson
    • 1
  • Leendert van der Torre
    • 2
  1. 1.Department of Computer ScienceKing’s CollegeLondonUK
  2. 2.Department of Artificial IntelligenceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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